An overview of fuzzy numbers and fuzzy arithmetic

The aim of this paper is to overview the field of fuzzy numbers and the arithmetic that has been developed to perform operations with fuzzy numbers. Issues concerning overestimation, shape preserving, properties and the expected intuitive characteristics of the operations are particularly emphasized. Recent revisions suggesting how to avoid discrepancies and pitfalls often observed in fuzzy arithmetic are discussed. These issues are of utmost relevance in many engineering, data processing and biological systems modeling and applications because fuzzy numbers are values for fuzzy variables. Moreover, when they are connected with linguistic concepts they provide meaning for values for linguistic variables, a key concept in the theory of fuzzy sets and fuzzy logic.